Rotor-Stator Interaction Analysis Using the Navier–Stokes Equations and a Multigrid Method

1996 ◽  
Vol 118 (4) ◽  
pp. 679-689 ◽  
Author(s):  
A. Arnone ◽  
R. Pacciani
Keyword(s):  
Stokes Equations ◽  
Interaction Analysis ◽  
Time Discretization ◽  
Navier Stokes ◽  
Implicit Time ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Fully Implicit ◽  
Rotor Stator Interaction ◽  
Stage Analysis

A recently developed, time-accurate multigrid viscous solver has been extended to the analysis of unsteady rotor–stator interaction. In the proposed method, a fully implicit time discretization is used to remove stability limitations. By means of a dual time-stepping approach, a four-stage Runge–Kutta scheme is used in conjunction with several accelerating techniques typical of steady-state solvers, instead of traditional time-expensive factorizations. The accelerating strategies include local time stepping, residual smoothing, and multigrid. Two-dimensional viscous calculations of unsteady rotor–stator interaction in the first stage of a modern gas turbine are presented. The stage analysis is based on the introduction of several blade passages to approximate the stator:rotor count ratio. Particular attention is dedicated to grid dependency in space and time as well as to the influence of the number of blades included in the calculations.

Rotor-Stator Interaction Analysis Using the Navier-Stokes Equations and a Multigrid Method

1995 ◽  
Author(s):  
Andrea Arnone ◽  
Roberto Pacciani
Keyword(s):  
Stokes Equations ◽  
Interaction Analysis ◽  
Time Discretization ◽  
Navier Stokes ◽  
Implicit Time ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Fully Implicit ◽  
Rotor Stator Interaction ◽  
Stage Analysis

A recently developed, time-accurate multigrid viscous solver has been extended to the analysis of unsteady rotor-stator interaction. In the proposed method, a fully-implicit time discretization is used to remove stability limitations. By means of a dual time-stepping approach, a four-stage Runge-Kutta scheme is used in conjunction with several accelerating techniques typical of steady-state solvers, instead of traditional time-expensive factorizations. The accelerating strategies include local time stepping, residual smoothing, and multigrid. Two-dimensional viscous calculations of unsteady rotor-stator interaction in the first stage of a modem gas turbine are presented. The stage analysis is based on the introduction of several blade passages to approximate the stator:rotor count ratio. Particular attention is dedicated to grid dependency in space and time as well as to the influence of the number of blades included in the calculations.

Multigrid Computations of Unsteady Rotor-Stator Interaction Using the Navier-Stokes Equations

1995 ◽  
Vol 117 (4) ◽  
pp. 647-652 ◽  
Author(s):  
A. Arnone ◽  
R. Pacciani ◽  
A. Sestini
Keyword(s):  
Stokes Equations ◽  
Time Discretization ◽  
Navier Stokes ◽  
Implicit Time ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Fully Implicit ◽  
Local Time Stepping ◽  
Rotor Stator Interaction ◽  
Residual Smoothing

A Navier-Stokes time-accurate solver has been extended to the analysis of unsteady rotor-stator interaction. In the proposed method, a fully-implicit time discretization is used to remove stability limitations. A four-stage Runge-Kutta scheme is used in conjunction with several accelerating techniques typical of steady-state solvers, instead of traditional time-expensive factorizations. Those accelerating strategies include local time stepping, residual smoothing, and multigrid. Direct interpolation of the conservative variables is used to handle the interfaces between blade rows. Two-dimensional viscous calculations of unsteady rotor-stator interaction in a modern gas turbine stage are presented to check for the capability of the procedure.

Implicit time-stepping methods for the Navier-Stokes equations

AIAA Journal ◽  
1996 ◽  
Vol 34 (3) ◽  
pp. 555-559 ◽  
Author(s):  
K. J. Badcock ◽  
B. E. Richards
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Implicit Time ◽  
Navier Stokes Equations ◽  
Time Stepping

scholarly journals Strong $L^2$ convergence of time numerical schemes for the stochastic two-dimensional Navier–Stokes equations

2018 ◽  
Vol 39 (4) ◽  
pp. 2135-2167 ◽  
Author(s):  
Hakima Bessaih ◽  
Annie Millet
Keyword(s):  
Stokes Equations ◽  
Random Perturbation ◽  
Time Discretization ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Exponential Moment ◽  
Navier Stokes Equations ◽  
Fully Implicit ◽  
Moment Estimates ◽  
Discretization Schemes

Abstract We prove that some time discretization schemes for the two-dimensional Navier–Stokes equations on the torus subject to a random perturbation converge in $L^2(\varOmega )$. This refines previous results that established the convergence only in probability of these numerical approximations. Using exponential moment estimates of the solution of the stochastic Navier–Stokes equations and convergence of a localized scheme we can prove strong convergence of fully implicit and semiimplicit temporal Euler discretizations and of a splitting scheme. The speed of the $L^2(\varOmega )$ convergence depends on the diffusion coefficient and on the viscosity parameter.

scholarly journals Artificial Compressibility Methods for the Incompressible Navier–Stokes Equations Using Lowest-Order Face-Based Schemes on Polytopal Meshes

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Riccardo Milani ◽  
Jérôme Bonelle ◽  
Alexandre Ern
Keyword(s):  
Stokes Equations ◽  
Time Discretization ◽  
Second Order ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Artificial Compressibility ◽  
Time Stepping ◽  
Monolithic Approach ◽  
Polytopal Meshes

Abstract We investigate artificial compressibility (AC) techniques for the time discretization of the incompressible Navier–Stokes equations. The space discretization is based on a lowest-order face-based scheme supporting polytopal meshes, namely discrete velocities are attached to the mesh faces and cells, whereas discrete pressures are attached to the mesh cells. This face-based scheme can be embedded into the framework of hybrid mixed mimetic schemes and gradient schemes, and has close links to the lowest-order version of hybrid high-order methods devised for the steady incompressible Navier–Stokes equations. The AC time-stepping uncouples at each time step the velocity update from the pressure update. The performances of this approach are compared against those of the more traditional monolithic approach which maintains the velocity-pressure coupling at each time step. We consider both first-order and second-order time schemes and either an implicit or an explicit treatment of the nonlinear convection term. We investigate numerically the CFL stability restriction resulting from an explicit treatment, both on Cartesian and polytopal meshes. Finally, numerical tests on large 3D polytopal meshes highlight the efficiency of the AC approach and the benefits of using second-order schemes whenever accurate discrete solutions are to be attained.

scholarly journals ON THE FLOW PAST RECTANGULAR CYLINDERS: PHYSICAL ASPECTS AND NUMERICAL SIMULATION

2008 ◽  
Vol 7 (1) ◽  
pp. 55 ◽  
Author(s):  
O. Almeida ◽  
S. S. Mansur ◽  
A. Silveira-Neto
Keyword(s):  
Incompressible Flows ◽  
Stokes Equations ◽  
Time Discretization ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Eddy Simulation ◽  
Fully Implicit ◽  
Side Ratio ◽  
Vortex Shedding Frequency ◽  
Rectangular Cylinders

This paper concerns with unsteady incompressible flows around rectangular cylinders with side ratio varying from 1 to 10. Phenomenological aspects are discussed and numerical simulations are performed using a SIMPLEC finite volume code. A third-order QUICK scheme is employed for the advective terms in the Navier-Stokes equations, while a second-order fully implicit method is used for the time discretization. For validation purpose, preliminary simulations are carried out at Re = 300. Afterwards, the flow patterns and the wake periodic features are examined at Re = 1,000, 5,000, and 22,000, for which turbulent effects should not be neglected. In some of those cases, large-eddy simulation (LES) is employed, using the classical sub-grid Smagorinsky model. Important physical mechanisms determining vortex shedding frequency are placed in evidence. The present predictions are compared with numerical and experimental results from other works and a good agreement is reached.

Sign in / Sign up

Export Citation Format

Share Document